package forth

/*
	在一个 n * m 的二维数组中，每一行都按照从左到右递增的顺序排序，每一列都按照从上到下递增的顺序排序。
	请完成一个高效的函数，输入这样的一个二维数组和一个整数，判断数组中是否含有该整数。
	示例:

	现有矩阵 matrix 如下：

	[
	  [1,   4,  7, 11, 15],
	  [2,   5,  8, 12, 19],
	  [3,   6,  9, 16, 22],
	  [10, 13, 14, 17, 24],
	  [18, 21, 23, 26, 30]
	]
	给定 target=5，返回true。

	给定target=20，返回false。

	限制：

	0 <= n <= 1000

	0 <= m <= 1000

	来源：力扣（LeetCode）
	链接：https://leetcode-cn.com/problems/er-wei-shu-zu-zhong-de-cha-zhao-lcof
	著作权归领扣网络所有。商业转载请联系官方授权，非商业转载请注明出处。
*/
func FindNumberIn2DArray(matrix [][]int, target int) bool {
	return findNumberIn2DArray(matrix, target)
}

func findNumberIn2DArray(matrix [][]int, target int) bool {
	if len(matrix) == 0 {
		return false
	}
	if len(matrix) == 0 {
		return false
	}
	return _findNumberIn2DArray(matrix, target, 0, len(matrix)-1, 0, len(matrix[0])-1)
}

func _findNumberIn2DArray(matrix [][]int, target int, start_row int, end_row int, start_col int, end_col int) bool {
	if start_row > end_row || start_col > end_col {
		return false
	}
	mid_row := (start_row + end_row) / 2
	mid_col := (start_col + end_col) / 2
	mid_num := matrix[mid_row][mid_col]
	if mid_num == target {
		return true
	}
	if mid_num > target {
		return _findNumberIn2DArray(matrix, target, start_row, mid_row-1, start_col, end_col) ||
			_findNumberIn2DArray(matrix, target, mid_row, end_row, start_col, mid_col-1)
	}
	return _findNumberIn2DArray(matrix, target, mid_row+1, end_row, start_col, end_col) ||
		_findNumberIn2DArray(matrix, target, start_row, end_row, mid_col+1, end_col)
}
